Machine learning for solving ill-conditioned Fredholm integrals.
problem Analytical continuation of quantum many-body physics spectra.
method Projected regression from a large database of solutions.
result Method performs as well or better than Maximum Entropy method.
New framework uses score-based priors to solve ill-conditioned polynomial equations, improving signal recovery from noisy data.
problem Recovering signals from low-order moments in inverse problems, especially ill-conditioned polynomial equations.
method Integrates score-based diffusion priors with moment-based estimators to regularize and solve nonlinear inverse problems.
result Diffusion priors improve recovery from third-order moments and make super-resolution MTD feasible.
Dual-space sampling tackles ill-conditioned inverse problems with Bayesian methods.
problem Bayesian inference in constrained inverse problems with ill-conditioned solutions.
method Dual-space posterior sampling using ADMM and SVGD.
result Well-calibrated uncertainty estimates and posterior contraction with increasing data.
Improves numerical solution of ill-conditioned linear systems for machine learning.
problem Wastefulness and instability in solving ill-conditioned linear systems.
method autonugget combines Richardson extrapolation to determine the solution of the ill-conditioned system, improving accuracy over a single nugget.
result Improves accuracy of numerical solution of ill-conditioned linear systems.
A new optimization method reduces memory and compute requirements for deep learning.
problem Memory and compute constraints in second-order stochastic optimizers for deep learning.
method Proposes KrAD, a novel factorization to approximate inverse Fisher matrix without inversion, leading to KrADagrad.
result Improves performance over Shampoo for 32-bit precision and comparable/generalization on real datasets.
Several methods have been recently proposed for estimating sparse Gaussian graphical models using ℓ1 regularization on the inverse covariance matrix. Despite recent advances, contemporary applications require methods that are even faster in order to handle ill-conditioned high dimensional modern day datasets. I…
AI-driven framework optimizes MCMC-based preconditioners for faster linear system solving.
problem Slow convergence of Krylov subspace solvers for ill-conditioned matrices.
method Graph neural surrogate and Bayesian optimization for AI-tuned MCMC parameters.
result 50% reduction in iterations to convergence on unseen system.
Regularizes 3D inverse scattering with tangent-point energy for better solutions.
problem Ill-conditioned inverse obstacle scattering problems in 3D.
method Tikhonov regularization using tangent-point energy to penalize surface roughness and ensure well-posedness.
result Regularized solutions converge to true solution as noise level decreases.
Nonlinear dimensionality reduction embeddings computed from datasets do not provide a mechanism to compute the inverse map. In this paper, we address the problem of computing a stable inverse map to such a general bi-Lipschitz map. Our approach relies on radial basis functions (RBFs) to interpolate the inverse map ever…
Paper introduces a new measure of conditional dependence avoiding matrix inversions.
problem Measuring conditional dependence between two phenomena influenced by a confounder.
method Uses U-statistics pruning to avoid matrix inversions and re-interpret independence.
result Proposes a novel measure of conditional dependence that avoids matrix inversions.
New approach improves deep learning robustness in medical imaging.
problem Deep learning models are vulnerable to adversarial examples in medical imaging.
method Propose a min-max learning scheme to generate adversarial examples and filter them out.
result Proposed method significantly improves robustness of deep learning models in medical imaging.
The paper addresses ill-conditioning in large spatial data, proposing solutions for prediction and likelihood estimation.
problem Ill-conditioning of the kernel matrix in large spatial data sets.
method Introduction of various optimality criteria and solutions for managing large spatial data.
result Solutions for managing large spatial data, addressing ill-conditioning and improving prediction and likelihood estimation.
The total variation (TV) penalty, as many other analysis-sparsity problems, does not lead to separable factors or a proximal operatorwith a closed-form expression, such as soft thresholding for the ℓ_1 penalty. As a result, in a variational formulation of an inverse problem or statisticallearning estimation, it l…
Scalable method completes ill-conditioned matrices from few samples.
problem Matrix completion from few samples for ill-conditioned matrices.
method Iterative algorithm combining IRLS, smoothing Newton, and proximal gradient methods.
result Local quadratic convergence rate and well-conditioned linear systems.
Paper shows linear convergence of ISTA and FISTA for ill-conditioned images.
problem Solving linear inverse problems with sparse representation in signal and image processing.
method Revisits iterative shrinkage-thresholding algorithms (ISTA) and improves their convergence properties.
result Linear convergence of ISTA and FISTA for strongly convex smooth parts, even in ill-conditioned cases.
Gaussian Processes (GPs) are a popular approach to predict the output of a parameterized experiment. They have many applications in the field of Computer Experiments, in particular to perform sensitivity analysis, adaptive design of experiments and global optimization. Nearly all of the applications of GPs require the …
New insights into adversarial vulnerability linked to manifold separability issues.
problem Adversarial vulnerability in machine learning models.
method Characterized data distribution as a low-dimensional manifold, focusing on on/off manifold directions and the impact of first-order vs. second-order optimization methods.
result First-order optimization methods lead to poor convergence in the off-manifold direction, causing adversarial vulnerability in inseparable datasets.
Paper explores challenges in training PINNs and loss landscape effects.
problem Challenges in training Physics-Informed Neural Networks (PINNs) due to loss landscape issues.
method Examined gradient-based optimizers Adam, L-BFGS, and their combination Adam+L-BFGS, and introduced NysNewton-CG (NNCG).
result Adam+L-BFGS outperforms other optimizers, and NysNewton-CG significantly improves PINN performance.
SAPPHIRE tackles ill-conditioned rERM problems with faster convergence.
problem Ill-conditioned objectives and non-smooth regularizers in rERM.
method Sketch-based preconditioning and scaled proximal mapping.
result Achieves condition-number-free linear convergence.
New methods improve portfolio risk minimization by estimating covariance matrix more accurately.
problem Uncertainty in estimating covariance matrix leads to unreliable hedge trades.
method Proposes two new estimators of the inverse covariance matrix using l2 and l1 norms.
result Portfolio formed using proposed estimators achieves substantial risk reduction and improved returns.
This paper analyzes adaptive gradient algorithms for better performance in ill-conditioned problems.
problem Poor performance of standard stochastic gradient algorithms in ill-conditioned problems.
method Non-asymptotic analysis of adaptive gradient algorithms (Adagrad and Stochastic Newton) for strongly convex objectives.
result Theoretical analysis and adaptation to practical applications like linear regression and regularized GLM.
New method stabilizes quantum Monte Carlo data analysis.
problem Noise in imaginary-time data impacts real-frequency spectra.
method Sparse modeling and regularization technique.
result Stable analytical continuation achieved with minimal bases.
Improved convergence for overparameterized low-rank matrix sensing.
problem Overparameterized low-rank matrix sensing with unknown rank and ill-conditioning.
method ScaledGD(λ) - preconditioned gradient descent method. result ScaledGD(λ) converges at a constant linear rate after a logarithmic number of iterations. Neural networks are vulnerable to adversarial examples due to ill-conditioned weight matrices.
problem Vulnerability of neural networks to adversarial examples.
method Used orthogonal regularization to ensure the weight matrix's condition number remains low.
result Orthogonal regularization increases adversarial accuracy on MNIST and F-MNIST datasets.
New method generates clean data from corrupted observations.
problem Generating clean data from corrupted observations.
method Iterative update of a transport map using black-box corruption channel access.
result Converges to a self-consistent transport map that effectively inverts the corruption channel.
Bayesian optimisation framework considers only variable orderings to handle ill-conditioned objectives.
problem Bayesian optimisation fails with ill-conditioned or discontinuous objectives.
method Proposes a new framework that considers only the ordering of variables in input and output spaces, fitting a Gaussian process in a latent space.
result Proves optimal performance under the measure of regret for an optimistic strategy in the latent space.
i-RevNet learns representations without discarding information, showing deep networks can generalize well.
problem The necessity of discarding uninformative variability in deep networks for good generalization.
method A cascade of homeomorphic layers that can be fully inverted, overcoming the ill-conditioned local inversion.
result i-RevNet can fully invert its representations, suggesting no information is discarded.
Scaled gradient descent improves matrix recovery for ill-conditioned matrices with optimal sampling complexity.
problem Recovering low-rank matrices from limited measurements efficiently and accurately.
method Scaled gradient descent (ScaledGD) with optimal sample complexity and improved iteration complexity.
result ScaledGD achieves optimal sample complexity and improved iteration complexity for ill-conditioned matrices.
New globally convergent Newton method tackles ill-conditioned generalized self-concordant losses.
problem Optimization of ill-conditioned generalized self-concordant losses in machine learning.
method Sequence of problems with decreasing regularization parameters, linear convergence with logarithmic condition number scaling.
result First large-scale algorithm with optimal generalization bounds for logistic and softmax regressions in non-parametric settings.
ScaledGD accelerates ill-conditioned low-rank estimation.
problem Slow convergence of gradient descent in ill-conditioned problems.
method Scaled gradient descent (ScaledGD) with preconditioning.
result Linear convergence rate independent of condition number.
Preconditioned SGD accelerates convergence for ill-conditioned huge-scale matrix completion.
problem Recovering a low-rank matrix from incomplete data with high condition number.
method Preconditioned Stochastic Gradient Descent (SGD) for huge-scale online optimization.
result Preconditioned SGD converges to ε-accuracy in O(log(1/ε)) iterations, compared to O(κlog(1/ε)) for unpreconditioned SGD.
Proposes an efficient shrinkage path for ridge regression.
problem Ill-conditioned data in linear models.
method A new generalized ridge regression shrinkage path that minimizes MSE risk.
result The path is as short as possible while maintaining optimal trade-off.
Kaczmarz++ accelerates convergence for ill-conditioned systems.
problem Solving ill-conditioned linear systems efficiently.
method Adaptive momentum acceleration, Tikhonov-regularized projections, and memoization.
result Kaczmarz++ converges faster than Krylov methods on ill-conditioned systems.
Neural operators correct PDE residuals to improve BIP solutions.
problem Reducing error in infinite-dimensional Bayesian inverse problems with neural operators.
method Error correction using PDE residuals to improve neural operator approximation.
result Trained neural operators with error correction achieve a quadratic reduction in approximation error.
RL accelerates portfolio optimization and option pricing by dynamically adjusting preconditioner sizes.
problem Large linear systems in portfolio optimization and option pricing lead to slow convergence.
method Reinforcement Learning (RL) dynamically adjusts block-preconditioner sizes to accelerate convergence.
result RL-driven solver significantly reduces computational cost and accelerates convergence.
Improved online gradient descent with fewer queries for dynamic environments.
problem Efficiently tracking changes in functions with varying gradients and smoothness.
method Developed a new theoretical framework to analyze online gradient descent in dynamic settings, reducing query complexity.
result Achieved state-of-the-art dynamic regret with significantly fewer gradient queries, independent of condition number.
This paper proposes a new method to quantify uncertainty in reservoir characterization using invertible neural networks.
problem Quantifying uncertainty in reservoir characterization models.
method Training an invertible neural network to represent the posterior distribution of model parameters.
result The proposed method provides a more efficient and direct way to sample from the posterior distribution.
Regularized LAEs learn principal components efficiently.
problem Learning optimal linear representations with LAEs.
method Proper regularization schemes (non-uniform ℓ2 and nested dropout).
result Convergence to optimal representation is slow due to ill-conditioning.
Improved subgradient method tackles ill-conditioned composite optimization problems.
problem Slow convergence of subgradient method for composite optimization problems.
method Preconditioned subgradient method with Levenberg-Marquardt approach.
result Linear convergence rate for composite optimization problems under mild conditions.
We orthogonalize the NSS model to condition and diagnose its ill-conditioned parameters.
problem The ill-conditioning of the NSS model's design matrix.
method Exact orthogonal reparametrization via QR decomposition.
result Orthogonalization isolates the conditioning structure and maintains fit uncertainty.
This paper accelerates distributed convex optimization by mitigating ill-conditioning issues.
problem Distributed convex optimization with ill-conditioned aggregate cost functions.
method Iterative pre-conditioning technique to improve convergence rate and stability.
result The proposed algorithm converges linearly with improved convergence rate and superlinearly under certain conditions.
Proposes a new metric selection for VM-PG with improved convergence.
problem Improves convergence of VM-PG methods for ill-conditioned problems.
method Diagonal Barzilai-Borwein stepsize for adaptive metric selection.
result Improved convergence results for ill-conditioned problems.
ScaledGD improves gradient descent for ill-conditioned low-rank matrix estimation.
problem Efficiently solving ill-conditioned low-rank matrix estimation problems.
method Scaled Gradient Descent (ScaledGD) with adaptive pre-conditioners.
result Linear convergence rate independent of condition number, low per-iteration cost.
New algorithms solve nonconvex-nonconcave minimax optimization problems.
problem Solving minimax optimization problems in machine learning.
method Two novel Newton-type algorithms for nonconvex-nonconcave minimax optimization.
result Proved local convergence at strict local minimax points.
Bayesian approach uses deep learning for seismic imaging and uncertainty quantification.
problem Uncertainty in seismic imaging due to nonuniqueness and noise.
method Implicit structured prior from randomly initialized convolutional neural network, combined with Bayesian model averaging and stochastic gradient Langevin dynamics.
result Deep priors reduce imaging artifacts and overfitting in noisy conditions.
New method solves sparse deconvolution problems with theoretical guarantees and practical applications.
problem Extracting localized, recurring motifs in signals with spatial or temporal structure.
method Geometric approach using sphere constraints and data-driven initialization to derive a provable algorithm.
result Practical algorithm solves real-world deconvolution problems with good performance and generalizability.
New method speeds up optimization over probability measures.
problem High computational overhead in optimizing probability measures.
method Randomized coordinate descent on Wasserstein space.
result Significant speedups over full-gradient methods.
New algorithm reduces sample complexity for sparse linear regression.
problem Sparse linear regression with correlated covariates and approximate dependencies.
method Polynomial-time algorithm that adapts the Lasso to tolerate approximate dependencies.
result Achieves near-optimal sample complexity for constant sparsity and ill-conditioned covariates.